Displacement measuring interferometers monitor changes in the position of a measurement object relative to a reference object based on an optical interference signal. The interferometer generates the optical interference signal by overlapping and interfering a measurement beam reflected from the measurement object with a reference beam reflected from the reference object.
Referring to FIG. 1, a typical interferometry system 10 includes a source 20, an interferometer 30, a detector 40, and an analyzer 50. Source 20 includes a laser for providing an input beam 25 to interferometer 30. In one example where heterodyne interferometry technique is used, input beam 25 includes two different frequency components having orthogonal polarizations. An acousto-optical modulator may be used to introduce frequency splitting to produce the two frequency components. Alternatively, source 25 may include a Zeeman-split laser to produce the frequency splitting. Alternatively, the different frequencies can be produced internal to the laser using birefringent elements. In another example where homodyne interferometry technique is used, input beam 25 may have a single wavelength.
In a heterodyne interferometry system, the orthogonally polarized components are sent to interferometer module 30, where they are separated into measurement and reference beams using a polarizing beam splitter (PBS). The reference beam travels along a reference path. The measurement beam travels along a measurement path. The reference and measurement beams are later combined by the PBS to form an exit beam 35 with overlapping exit measurement and reference beams. In a homodyne interferometry system, a non-polarizing beam splitter may be used to separate the input beam into the measurement and reference beams.
Exit beam 35 subsequently passes through a polarizer (not shown). The polarizer mixes polarizations of the exit measurement and reference beams to form a mixed beam. Components of the exit measurement and reference beams in the mixed beam interfere with one another so that the intensity of the mixed beam varies with the relative phase of the exit measurement and reference beams. The interference contains information about the relative difference in optical path length between the reference and measurement paths.
In one example, the reference path is fixed and the changes in the optical path length difference correspond to changes in the optical path length of the measurement path. In another example, the optical path length of both the reference and measurement paths may change, e.g., the reference path may contact a reference object that moves relative to interferometer module 30. In this case, changes in the optical path length difference correspond to changes in the position of the measurement object relative to the reference object.
Detector 40 includes a photodetector that measures the time-dependent intensity of the mixed beam and generates an electrical interference signal proportional to that intensity. Detector 40 may also include electronic components (e.g., an amplifier and an analog-to-digital converter) that amplifies the output from the photodetector and produces a digital signal corresponding to the optical interference.
When the measurement and reference beams have different frequencies, the electrical interference signal includes a “heterodyne” signal having a beat frequency equal to the difference between the frequencies of the exit measurement and reference beams. If the lengths of the measurement and reference paths are changing relative to one another, e.g., by translating a stage that includes the measurement object, the measured beat frequency includes a Doppler shift equal to 2vnp/λ, where v is the relative speed of the measurement and reference objects, λ is the wavelength of the measurement and reference beams, n is the refractive index of the medium through which the light beams travel, e.g., air or vacuum, and p is the number of passes to the reference and measurement objects. Changes in the relative position of the measurement object correspond to changes in the phase of the measured interference signal, with a 2π phase change substantially equal to a distance change L of λ/(np), where L is a round-trip distance change, e.g., the change in distance to and from a stage that includes the measurement object.
Unfortunately, this equality is not always exact. In addition, the amplitude of the measured interference signal may be variable. A variable amplitude may subsequently reduce the accuracy of measured phase changes. Many interferometers include non-linearities such as what are known as “cyclic errors.” The cyclic errors can be expressed as contributions to the phase and/or the intensity of the measured interference signal and have a sinusoidal dependence on the change in optical path length pnL. In particular, the first harmonic cyclic error in phase has a sinusoidal dependence on (2πpnL)/λ and the second harmonic cyclic error in phase has a sinusoidal dependence on 2 (2πpnL)/λ. Higher harmonic cyclic errors can also be present.
There are also “non-cyclic non-lineaties” such as those caused by a change in lateral displacement (i.e., “beam shear”) between the reference and measurement beam components of an output beam of an interferometer when the wavefronts of the reference and measurement beam components have wavefront errors. This can be explained as follows.
Inhomogeneities in the interferometer optics may cause wavefront errors in the reference and measurement beams. When the reference and measurement beams propagate collinearly with one another through such inhomogeneities, the resulting wavefront errors are identical and their contributions to the interferometric signal cancel each other out. More typically, however, the reference and measurement beam components of the output beam are laterally displaced from one another, i.e., they have a relative beam shear. Such beam shear causes the wavefront errors to contribute an error to the interferometric signal derived from the output beam.
Moreover, in many interferometry systems beam shear changes as the position or angular orientation of the measurement object changes. For example, a change in relative beam shear can be introduced by a change in the angular orientation of a plane mirror measurement object. Accordingly, a change in the angular orientation of the measurement object produces a corresponding error in the interferometric signal.
The effect of the beam shear and wavefront errors will depend upon procedures used to mix components of the output beam with respect to component polarization states and to detect the mixed output beam to generate an electrical interference signal. The mixed output beam may for example be detected by a detector without any focusing of the mixed beam onto the detector, by detecting the mixed output beam as a beam focused onto a detector, or by launching the mixed output beam into a single mode or multi-mode optical fiber and detecting a portion of the mixed output beam that is transmitted by the optical fiber. The effect of the beam shear and wavefront errors will also depend on properties of a beam stop should a beam stop be used in the procedure to detect the mixed output beam. Generally, the errors in the interferometric signal are compounded when an optical fiber is used to transmit the mixed output beam to the detector.
Amplitude variability of the measured interference signal can be the net result of a number of mechanisms. One mechanism is a relative beam shear of the reference and measurement components of the output beam that is for example a consequence of a change in orientation of the measurement object.
In dispersion measuring applications, optical path length measurements are made at multiple wavelengths, e.g., 532 nm and 1064 nm. The measurements are used to determine dispersion of the beams as they travel through a gas in the measurement path. The dispersion measurement can be used in converting the optical path length measured by a distance measuring interferometer into a physical length. Such a conversion can be important since changes in the measured optical path length can be caused by gas turbulence and/or by a change in the average density of the gas in the measurement arm even though the physical distance to the measurement object is unchanged.